Shock calculations for axially symmetric shear wave propagation in a hyperelastic incompressible solid

摘要

Breaking distance and time are calculated for axially symmetric shear waves in an incompressible hyperelastic solid, whose strain energy function is expressible as a truncated power series in terms of the basic strain invariants. Waves are generated by the application of tractions at the surface of a cylindrical cavity in an unbounded medium. Approximate formulas are developed for the characteristics of the governing system of hyperbolic partial differential equations. Using these formulas, the breaking time of a shock wave is calculated and the location of the shock path is estimated. The shock analysis carried out here provides insight into how the material parameters influence shock development. In order to test the validity of our shock calculations, numerical solutions are obtained using a relaxation scheme for systems of conservation laws.